Highest Common Factor of 577, 838, 172 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 577, 838, 172 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 577, 838, 172 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 577, 838, 172 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 577, 838, 172 is 1.

HCF(577, 838, 172) = 1

HCF of 577, 838, 172 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 577, 838, 172 is 1.

Highest Common Factor of 577,838,172 using Euclid's algorithm

Highest Common Factor of 577,838,172 is 1

Step 1: Since 838 > 577, we apply the division lemma to 838 and 577, to get

838 = 577 x 1 + 261

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 261 and 577, to get

577 = 261 x 2 + 55

Step 3: We consider the new divisor 261 and the new remainder 55, and apply the division lemma to get

261 = 55 x 4 + 41

We consider the new divisor 55 and the new remainder 41,and apply the division lemma to get

55 = 41 x 1 + 14

We consider the new divisor 41 and the new remainder 14,and apply the division lemma to get

41 = 14 x 2 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 577 and 838 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(261,55) = HCF(577,261) = HCF(838,577) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 172 > 1, we apply the division lemma to 172 and 1, to get

172 = 1 x 172 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 172 is 1

Notice that 1 = HCF(172,1) .

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Frequently Asked Questions on HCF of 577, 838, 172 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 577, 838, 172?

Answer: HCF of 577, 838, 172 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 577, 838, 172 using Euclid's Algorithm?

Answer: For arbitrary numbers 577, 838, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.